Introduction to Logic
Use the Fitch System to prove ((p ⇒ q) ⇒ p) ⇒ p.
Show Instructions
To apply a rule of inference, check the lines you wish to use as premises and click the button for the rule of inference. Reiteration allows you to repeat an earlier item. To delete one or more lines from a proof, check the desired lines and click Delete. When entering expressions, use Ascii characters only. Use ~ for ¬; use & for ∧; use  for ∨; use => for ⇒; use <=> for ⇔.
1
(p => q) => p
Assumption
2
~p
Assumption
3
p
Assumption
4
~q
Assumption
5
p
Reiteration
3
6
~q => p
Implication Introduction
4
5
7
~q
Assumption
8
~p
Reiteration
2
9
~q => ~p
Implication Introduction
7
8
10
~~q
Negation Introduction
6
9
11
q
Negation Elimination
10
12
p => q
Implication Introduction
3
11
13
~p => p => q
Implication Introduction
12
14
~p
Assumption
15
p => q
Assumption
16
~p
Reiteration
14
17
(p => q) => ~p
Implication Introduction
15
16
18
~(p => q)
Negation Introduction
1
17
19
~p => ~(p => q)
Implication Introduction
14
18
20
~~p
Negation Introduction
13
19
21
p
Negation Elimination
20
22
((p => q) => p) => p
Implication Introduction
1
21
